On the other hand, signals or images in optical information theory may be
described directly or indirectly by the Wigner distribution function (WDF)
[1]}. In one-dimensional (1D) case, the WDF of an optical signal field \(\psi \left( x\right) \)  is defined as
\(W_{\psi }(\nu ,x)=\int _{-\infty }^{+\infty }\frac{\mathtt {d}u}{2\pi }e^{\mathtt {i}\nu u}\psi ^{\ast }\left( x+\frac{u}{2}\right) \psi \left( x-\frac{u}{2}\right) . \) 
